Pythagorean Geometry in Vedic-era Texts

The position paper, part of Karnataka’s submissions to the NCERT for a National Curriculum Framework, has revived discussion on what we call the Pythagoras theorem was already known to Indians from the Vedic times.

Context

The position paper, part of Karnataka’s submissions to the NCERT for a National Curriculum Framework, has revived discussion on what we call the Pythagoras theorem was already known to Indians from the Vedic times.

Dispute

• The Pythagoras theorem is disputed in many international forums. Not the content, but Pythagoras claiming it as his own.
• A retired IAS officer who heads Karnataka’s NEP task force, has referred to a text called the BaudhayanaSulbasutra, in which a specific shloka refers to the theorem.

Pythagoras History

• Evidence suggests that the Greek philosopher (around 570–490 BC) did exist.
• There is an element of mystery around him, largely because of the secretive nature of the school/society he founded in Italy.
• Relatively little is known about his mathematical achievements, because there is nothing today of his own writings.

About Pythagoras Theorem

• The Pythagoras theorem describes the relationship connecting the three sides of a right triangle(one in which one of the angles is 90°).
• a² + b² = c²
• If any two sides of a right triangle are known, the theorem allows you to calculate the third side.
  

What is the evidence that Sulbasutra contains?

• In the first chapter in the BaudhayanaSulbasutra contains, the (areas of the squares) produced separately by the length and the breadth of a rectangle together equal the area (of the square) produced by the diagonal.
• This is observed in rectangles having sides 3 and 4, 12 and 5, 15 and 8, 7 and 24, 12 and 35, 15 and 36.

Uses

• The yajna rituals involved construction of altars (vedi) and fireplaces (agni) in a variety of shapes such as isosceles triangles, symmetric trapezia, and rectangles.
• The sulbasutras describe steps towards construction of these figures with prescribed sizes.

What is the similarity between Sulbasutra’s equation and Pythagoras?

• The Pythagorean equation comes into play in these procedures, which involve drawing perpendiculars.
• These perpendiculars were based on triangles whose sides were in the ratio 3:4:5 or 5:12:13.
• These sides follow the Pythagorean relation, because 3² + 4² = 5², and 5² + 12² = 13². Such combinations are called Pythagorean triples.